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Math Help - Basis

  1. #1
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    Basis

    I have no idea how to start solving this problem. My professor gives really bad notes. I know you guys dont like to work problems without the asker doing some work, but i dont know where to start. If someone could walk me through this i would greatly appreciate it.

    I dont know how to format matrices so i just copied the problem from the website. Each set of numbers in parentheses should be in a 1 column matrix (top, bottom).

    Any help is greatly appreciated.

    Consider the basis of consisting of vectors
    (-2, 5) and (-5, 4) .
    Find in whose coordinate vector relative to the basis is
    (-1, 6) .
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  2. #2
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    You want to solve <br />
a\left[ \begin{gathered}<br />
   - 2 \hfill \\<br />
  3 \hfill \\ <br />
\end{gathered}  \right] + b\left[ \begin{gathered}<br />
   - 5 \hfill \\<br />
  4 \hfill \\ <br />
\end{gathered}  \right] = \left[ \begin{gathered}<br />
   - 1 \hfill \\<br />
  6 \hfill \\ <br />
\end{gathered}  \right]

    or \left\{ \begin{gathered}<br />
   - 2a - 5b =  - 1 \hfill \\<br />
  5a + 4b = 6 \hfill \\ <br />
\end{gathered}  \right.
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  3. #3
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    I used substition and got a=26/17 and b=-7/17.

    Is that my answer? Cause the website is telling me it's wrong.
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  4. #4
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    Well the way you have formated the question makes it very hard to read.
    I may not have understood what is being asked.

    Do you do correctly?
    Attached Thumbnails Attached Thumbnails Basis-untitled.gif  
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  5. #5
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    Here's a screenshot of the question. It looked like you had understood it correctly.


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  6. #6
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    See if this is what is meant by that wording.
    Attached Thumbnails Attached Thumbnails Basis-untitled.gif  
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  7. #7
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    Awesome! That worked. Could you explain how that works, cause i was certain that i was solving for an a and b like you had originally said.
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  8. #8
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    Quote Originally Posted by manofsteele888 View Post
    Could you explain how that works, cause i was certain that i was solving for an a and b like you had originally said.
    Well I am not sure I can.
    The way that question is worded is missleading I think.
    But I am not someone who regularly works with linear algebra wording.
    Perhaps someone else here can explain that wording.
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  9. #9
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    Ok, thanks man. Much appreciated.
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  10. #10
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    Quote Originally Posted by manofsteele888 View Post
    I have no idea how to start solving this problem. My professor gives really bad notes. I know you guys dont like to work problems without the asker doing some work, but i dont know where to start. If someone could walk me through this i would greatly appreciate it.

    I dont know how to format matrices so i just copied the problem from the website. Each set of numbers in parentheses should be in a 1 column matrix (top, bottom).

    Any help is greatly appreciated.

    Consider the basis of consisting of vectors
    (-2, 5) and (-5, 4) .
    Find in whose coordinate vector relative to the basis is
    (-1, 6) .

    .
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